#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #define forr(x,arr) for(auto&& x:arr) #define _overload3(_1,_2,_3,name,...) name #define _rep2(i,n) _rep3(i,0,n) #define _rep3(i,a,b) for(int i=int(a);i=int(a);i--) #define rrep(...) _overload3(__VA_ARGS__,_rrep3,_rrep2,)(__VA_ARGS__) #define all(x) (x).begin(),(x).end() #define bit(n) (1LL<<(n)) #define sz(x) ((int)(x).size()) #define TEN(n) ((ll)(1e##n)) #define fst first #define snd second string DBG_DLM(int &i){return(i++==0?"":", ");} #define DBG_B(exp){int i=0;os<<"{";{exp;}os<<"}";return os;} templateostream&operator<<(ostream&os,vectorv); templateostream&operator<<(ostream&os,setv); templateostream&operator<<(ostream&os,queueq); templateostream&operator<<(ostream&os,priority_queueq); templateostream&operator<<(ostream&os,pairp); templateostream&operator<<(ostream&os,mapmp); templateostream&operator<<(ostream&os,unordered_mapmp); templatevoid DBG(ostream&os,TPL t){} templatevoid DBG(ostream&os,TPL t){os<<(I==0?"":", ")<(t);DBG(os,t);} templatevoid DBG(ostream&os,pairp,string delim){os<<"("<ostream&operator<<(ostream&os,tuplet){os<<"(";DBG<0,tuple,Ts...>(os,t);os<<")";return os;} templateostream&operator<<(ostream&os,pairp){DBG(os,p,", ");return os;} templateostream&operator<<(ostream&os,vectorv){DBG_B(forr(t,v){os<ostream&operator<<(ostream&os,sets){DBG_B(forr(t,s){os<ostream&operator<<(ostream&os,queueq){DBG_B(for(;q.size();q.pop()){os<ostream&operator<<(ostream&os,priority_queueq){DBG_B(for(;q.size();q.pop()){os<ostream&operator<<(ostream&os,mapm){DBG_B(forr(p,m){os<");});} templateostream&operator<<(ostream&os,unordered_mapm){DBG_B(forr(p,m){os<");});} #define DBG_OVERLOAD(_1,_2,_3,_4,_5,_6,macro_name,...)macro_name #define DBG_LINE(){char s[99];sprintf(s,"line:%3d | ",__LINE__);cerr<;using pll=pair;using pil=pair;using pli=pair; using vs=vector;using vvs=vector;using vvvs=vector; using vb=vector;using vvb=vector;using vvvb=vector; using vi=vector;using vvi=vector;using vvvi=vector; using vl=vector;using vvl=vector;using vvvl=vector; using vd=vector;using vvd=vector;using vvvd=vector; using vpii=vector;using vvpii=vector;using vvvpii=vector; templatebool amax(A&a,const B&b){return b>a?a=b,1:0;} templatebool amin(A&a,const B&b){return b>l;return l;} string rs(){string s;cin>>s;return s;} template bool is_prime_impl(const uint64_t &n, const uint64_t *witness, BinOp modmul) { if (n == 2) return true; if (n < 2 || n % 2 == 0) return false; const int64_t m = n - 1, d = m / (m & -m); auto modpow = [&](int64_t a, int64_t b) { int64_t res = 1; for (; b; b /= 2) { if (b & 1) res = modmul(res, a); a = modmul(a, a); } return res; }; auto suspect = [&](uint64_t a, uint64_t t) { a = modpow(a, t); while (t != n - 1 && a != 1 && a != n - 1) { a = modmul(a, a); t = modmul(t, 2); } return a == n - 1 || t % 2 == 1; }; for (const uint64_t *w = witness; *w; w++) { if (*w % n != 0 && !suspect(*w, d)) return false; } return true; } bool is_probable_prime(const uint64_t &n) { assert(n < (1ULL << 63)); if (n < (1ULL << 32)) { constexpr uint64_t witness[] = {2, 7, 61, 0}; auto modmul = [&](uint64_t a, uint64_t b) -> uint64_t { return a * b % n; }; return is_prime_impl(n, witness, modmul); } else { constexpr uint64_t witness[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022, 0}; auto modmul = [&](uint64_t a, uint64_t b) -> uint64_t { return (uint64_t)((__uint128_t)a * b % n); }; return is_prime_impl(n, witness, modmul); } } void Main() { ll n = ri(); cout << n << ' ' << is_probable_prime(n) << '\n'; } signed main() { cin.tie(nullptr); ios::sync_with_stdio(false); int T;cin>>T; while (T--) Main(); return 0; }